6. 已知$x + 2y - 1 = 0$，求代数式$\frac{2x + 4y}{x^2 + 4xy + 4y^2}$的值.

解：​ x + 2y - 1 = 0，​则​x + 2y = 1。​
故原式$​=\frac {2(x + 2y)}{(x + 2y)^2} = \frac {2}{x + 2y}$。​
将​x + 2y = 1​代入，得$​\frac {2}{1} = 2$。​

7. 将$a\ \mathrm{g}$盐放入$b\ \mathrm{g}$水中，得到的盐水中盐的浓度为$\frac{a}{a + b}$，将三杯浓度相同、质量不同的盐水混合，根据生活经验，浓度好像不变，如何证明这个结论呢？请解答下列问题：
已知$\frac{a}{a + b} = \frac{c}{c + d} = \frac{e}{e + f} = k$，求证$\frac{a + c + e}{a + b + c + d + e + f} = k$.

解：因为$​\frac {a}{a + b} = k$，​所以​a = k(a + b)；​
同理$​\frac {c}{c + d} = k​$得​c = k(c + d)，$​​\frac {e}{e + f} = k​$得​e = k(e + f)。​
则​a + c + e = k(a + b) + k(c + d) + k(e + f) ​
​= k[(a + b) + (c + d) + (e + f)]。​
因此$​\frac {a + c + e}{a + b + c + d + e + f} = \frac {k[(a + b) + (c + d) + (e + f)]}{(a + b) + (c + d) + (e + f)} = k$。​